Arithmetical drill-card.



y H. D. RICKARD. ARITHMETICAL DRILL CARD. APPLICATION FILED FEB. s. |915.

Patented Aug. 17, 1915.

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H. D. RICKABD.

ARITHMETICAL DRILL CARD.

APPLICATION FILED FEB. 9, i915. Y

Patented mig. 17, 1915.

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n Honnoan. RICKARD, or sYRAoUsE, NEW YORK.

ARITHMETICAL DRILL-CARD.

Specica'tion of Letters Patent.

Patented Aug. 17, 1915.

application ined February 9, 1915. seran No. 6,975.

T all whom 'it may concern Be it known that I, HORACE D. RICHARD,

l a citizen of the United States, and resident of Syracuse, in the county of Onondaga, in the State of New York, haverinvented new and useful. Improvements 1n Arithmetical Drill-Cards, of which the following, taken in connection with the accompanying drawings, is a full, clear, and exact description.

This invention relates to certain improvements in arithmetical drill cards adapted to be used in grammar schools and other educational institutions for drilling and disciplining the minds of the students in the fundamental problems of mathematics, but it is evident that the same device may be used for the same purpose or for competitive tests of skill by individuals or groups in the home or in other places where such discipline or competitive tests may be of interest.

The main object is to bring together upon one face of a card of suitable size for convenience in handling a relatively large number of numerical factors so arranged that "they be visually associated and mentallycomputed in different problems.

Another object is to provide the card with a rotary sectionfbearing a circular row of numerals capable of Abeing presented one at a time into registration with a sight opening in the card so that such numeral may be associated with any one of the other numerals appearing upon the face of the card for mental computation.

A further object is to provide the reverse side of the card with separatecolumns of numerical results of such computations un- 1 der separate numerical headings corresponding to those on the dial or rotary disk.

still further object is to space the numerical results of each column to correspond with the spacings of the numerical factors on the obverse side of the card so that the student-may place upon a separate sheet opposite those factors the results of each computation and then register the temporary results with the corresponding lines in the result column under the numerical head corresponding to that on the disk which is used in such computations.

Another object is to provide the same card with a plurality of numbered disks andV sight-openings through which the numbers individually appear and a corresponding number of columns of factors reversely arranged on the obverse face andto also provide on the reverse face of the card a corresponding number of sets of columns of numerical results of the computations involving the various combinations of factors appearing in the columns on the obverse face and disks.

Other objects and uses will appear from the following description.

In the drawings Figures l and 2 are opposite face views of one-of the cards as used for adding integers. -F igs. 3 and 4c are opposite faceviews of a similar card used for mental drill in multiplication of integers. Figs. 5 and G are opposite face views of another card for mental drill in subtraction of fractions, and Figs. 7 and 8 are opposite face views ofa similar card for mental computations in division of fractions. Fig. 9 is an enlarged sectional view through a portion of one of the cards and disks showing the pivotal eyelet for said disk and the sightopening across which the numbers on the disk are adapted to be registered.

I have shown a yseries offour cards only for the vpurpose of illustrating how they may be used in mental drilling in the fundamental branches of arithmetic, such as for example, addition, subtraction, multiplication and division, but it is evident that the vnumber of cards may be multiplied for other branches of mathematics, each card being preferably of the same form, size and material so thatl they may be stacked in book form and used in disciplining or drilling the student in any selected branch of mathematics.

Asillustrated, each device consists of an elongated substantially rectangular sheet -1- of cardboard or equivalent comparatively inexpensive material suitable for the purpose and of such size as to be conveniently handled in class or individual work, and aside from the differences in numerals and computations, the description of the structure of one card will serve for all. Each card is provided on its reverse side near diagonally opposite corners with separate rotary disks -2 centrally secured thereto by pivotal eyelets 8-' to permit them to be turned by hand, each disk bearing on its obverse face a circular row of numerical factors, those von each disk representing progressively varying valuesV arranged in sequence for registration one by one with a suitable sight-opening in the card as the disk is rotated so as to appear on the obverse face thereof.

ln the cards for drilling the student in addition of whole numbers, as shown in Figs. l and 2, the numerals l to 9 inclusiveY thereby render the computation of each value appearing in the column with that appearing on the disk entirely independent of any other combinations. lt will be observed, however, that l have placed in both columns combined all of the integers from one to fifty inclusive, thus producing four hundred and fifty different combinations of numerical factors or problems in addition in a single card. lt is evident, however, that the number and value of these factors both of the columns and in the disk may be varied without departing from the spirit of my invention so long as these factors in the columns are equally spaced to correspond with the spacings of the numerical results appearing on the reverse side of the card.

@n the reverse side of the card, is printed or otherwise impressed two sets of columns of nume ical results, the number of columns in each set corresponding to the number of factors on the corresponding disk, in this instance -9-, each column being designated by a numerical factor corresponding to that on the disk used in producing the resulL appearing in that column, the headings of the columns of each set being preferably numbered from left to right and from one to nine, inclusive, while the factors appearing in the several columns of each set are arranged'in horizontal lines, spaced vertically 'to correspond with the spacings of the column of factors appearing on the obverse side, so that the numerals appearing in any one line are the results of the computations of the corresponding factor in the same position on the obverse side of the card with each numerical factor on the disk. For example, assuming that the numeral -lon the disk is registered with the sight-opening in the card, as shown in Fig. l, and that it is desired to add this to the first numeral appearing in the column 5--, the n n result 08H will then be round in the irst line of the corresponding column on the reverse side of the card under the numeral -4 ln like manner, suppose it is desired to add the numeral Llappearing on the disk to the numeral 45tappearing in the right hand column, Fig. l; then the result -/l8- will appear in the same line under the heading aon the reverse side of the card in the corresponding set of columns. Again as another example, suppose, it is desired to add the factor 9 on the disk to the numeral 13 in the column on the obverse side of the card, Fig. l, in which case the disk would be rotated by hand until the numeral -9- appears at the sightopening, whereupon the result 2Q- will be found on the reverse side of the card in the same line as the numeral -13-, but under the heading -9`-. The numerals in the columns in the central portion yon the reverse side of the card have been omitted in order to avoid excessive labor and confusion, but it is to be understood that these numerals will be printed in to complete the results for each numeral in the columns -5- and -5- on the obverse side of the card in horizontal alineinent therewith.

The device shown in Figs. 3 and l is for drilling the student in multiplication, and aside from the numerals which are printed or otherwise impressed on the obverse and reverse sides of the card and also on the obverse side of the disk, the structure is substantially thesame as that shown in Figs. l and 2. ln this multiplication card, one of the disks bears a circular row of numbers from one to six, inclusive, while the other disk bears the same number of numerals numbered from seven to twelve, inclusive, said numerals being adapted to be individually registered with their respective sightopenings as their corresponding disks are turned. Associated with each disk is a column of, in this instance, twenty-five, numerals arranged in reverse order in the same manner as shown in Fig. l, except that their values range from one to twelve, inclusive, sonic of the numerals being of the saine value to permit them to be combined with different numerals appearing on the corresponding disks. ln other words, this particular card is for drilling the student in multiplying all numbers ranging in value from' one to twelve. rThe results of these combinations appear in their respective columns on the reverse side of the sheet or card under the numerical headings corresponding to that on the disk which may be registered withy the sight-opening, the spacings of the 'numerals in the several columns on the reverse side corresponding with those on the obverse side. For example, assuming that it is desired to verify the result of multiplyingeleven 'by eleven, as shown in Fig. 3; then by referring to the reverse side 'of the card under the heading -llwill'be found the result or product one hundred and twenty-one, or if it is desired to verify the result of any other numeral as six multiplied, say by twelve, in the corresponding column, the result seventy-two will be found under the heading siX'in horizontal alinement with the numeral twelve on the reverse side of the card. in like manner, the result of any other combination of factors may be readily ascertained or verified. lt Will be observed that this multiplication card provides for three hundred different examples whichmight be varied at Will by changing nber of numerals upon the dials or in ,inns on the obverse side and making corresponding variations in the columns of results on the reverse side, all of which is entirely Within lthe scope of my present invention.

Y rThe device shown in Figs. 5 and 6 is for drilling the student in subtraction of fractions'and the columns of numerals on the obverse and reverse sides of the card are arranged in substantially the same manner shoivn iu Figs. l to '-i, inclusive, While the dis rs --2- are provided with circular roivs of fractional factors movable individually into registration with their respective sight- Y openings .ln the use of these subtraction cards, the results ofthe combination of the fraction on the disk With any one of the fractions or Whole numbers appearing in the corresponding column on the obverse side viill be found on the reverse side of the card in line With that particular fractionA or ivhole number, under the numerical heading corresponding to that'on the disk registered With the sight-opening. F or example, assuming that it is desired to take l/Q from 3/5 appearing on the obverse si I the result, l/r-O, will be found in line with the fraction 3/5 under the heading 1/2. ln like manner, if it is desired to take 1/8 from 7/10, the disk will be turned to register the fraction l/S with the sight-opening -iafter which the result, 23/40, will be found in line with the numerical value7/10 under the heading 1/8. In a similar manner any one of the fractions appearing on either of the disks may be taken from any one of the fractions or Whole numbers appearing in the corresponding column and the result ascertained under the heading corresponding to that on the disk and in line with the factor in the column on the obverse side of the card. It will be seen from the foregoing description that this subtraction card comprehends the same number, four hundred fifty, of examples as that shown in Figs. l and 2.

The card shown in Figs. 7 and 8 is for drilling the student in division of fractions, and is provided on its obverse face with columns of numerical fractions arranged in substantially the same manner as those shown in Figs. 5 and 6, but of different Values most suitable in drilling in this branch of mathematics, the reverse side of the card being provided with separate sets of columns of results or quotients arranged in a manner similar to those on the reverse sides of the previously described cards, the disks being also provided with circular rows of numerical fractions for registration with their respective sight-openings ln this instance, each disk bears a series of siX factors, and therefore, there are six columns in each set on the reverse side of the card spaced in lines coi-respondng` to the spacings on the obverse side, so that the result of dividing any one of the factors appearing in the column on the obverse side of the card by the factor appearing on the corresponding disk through its sight-opening will appear on the reverse side of the card in line With the first named factor under the heading corresponding With that on the disk.

For example, assuming that it is desired to to obtain the quotient of 6/11 divided by M5, then the result, 153/22 will appear under the heading l/ and in the line correspond ing With the factor ti/ll. lt is, of course, obvious that it is not necessary to have the esults printed on the reverse side of the card exactly oppositethe factor in the column on the obverse side of the card used in producing such result, the only requirement being that the spacings of the numerals in the result columns siall correspond with the spacing of the factors the column on the obverse side of the card. his division card also comprehends the same number, three hundred, examples of different combinations as the multiplica tion card.

It is, therefore, evident from the foregoing description that each card, although relatively small and easily handled, provides for a large number of combinations of factors and a corresponding number of results of such computations, the factors for each card being selected to afford tie most effective drill and discipline in mental calculations or mental arithmetic.

What l claim is:

1. An educational device comprising lli) card or plate having a column of numerical f factors on one face, a revoluble disk thereon having a circular rovv of numerical factors adapted to be brought to view one at a `time to said face, said card having printed on its opposite face a series of columns of numerical results of mathematically combining each factor on t-he disk with each factor in the column, the result columns correspondfactors on its obverse face arranged in equally spaced relation, a revoluble disk mounted on the card and provided With a circular row of numerical factors adapted to be registered one at a time with a sightopening in the obverse face of the card, and a series of coluimis of numerical results impressed on the reverse side of the card corresponding in number to the number of factors on the di slr and designated numerical headings corresponding to said factors, the numerical results in each column being spaced to correspond to the spacings of the numerical factors in the first named column and in the same order.

3. An educational device comprising a card or plate having a numerical factor on its obverse face, a rotary dislr having a circular roiv of numerical factors adapted to be registered one at a time with a sigl t-opening in the obverse face of the card or pla-te, said factors on the dislr being reproduced in a horizontal line on the reverse side of the card or plate, and numerical results of mathematically combining said factors impressed upon the reverse side of the card or plate under the horizontal line of factors used in obtaining those results.

la An educational device comprising a card or plate having ay column of numerical factors impressed upon its obverse face and arranged in equally spaced relation, a rotary disk mounted on the plate and provided with numerical factors registrable one at a 'time only with a sight opening in the obverse side of the card or plate, a column of numerical results on the r-verse side of the plate corresponding to the factor on the dislr and designated by a heading corresponding to such dislr factor, the numerical results in the result column being spaced to correspond to the spacings of the numerical factors in the first named column and in the same order.

ln an educational device of the character described, a card or plate having a set of numerical factors on one face, means for displaying another set of factors one at a time at the same face, each factor of one set being adapted to be mathematically combined with each of the factors of the other et, the numerical results of such combinaions being impressed on the opposite face of the card in columns under headings corresponding to the factors in the second named set and in the order of arrangement of the factors of the first named set.

6. In an educational device of the character described, a card or plate and a movable member 'thereon bearing a group of different numeri al factors and cooperating with the card or plate for displaying said factors one only at a time to one face of the card, said card having a column of numerical factors on the sa ne face to which one of the factors of the group is displayed, and cach adapted to be mathematically combined With each of the factors of said group for producing num rical results, said results being printed in columns on the opposite side of the card under num rical headings corresponding to those appearing in the group.

7. ln an educational device of the character described, a card or plate and a movs able member thereon bearing a group of different numerical factors and cooperating therewith for displaying said factors one only at a time to one face of the card and concealing the remaining factors of said group, said face having also impressed thereon a column of numerical factors, each adapted to be mathematically combined with each of the factors of the group for producing mathematical results, said results being impressed on the opposite face of the card in separate columns corresponding in number .to the number of factors in said group and the number of numerical results appearing in each column corresponding to the number of factors appearing in the first named column.

ln Witness whereof l have hereunto set lny hand this 30th day of January, 1915.

HRACE' l). RCKARD,

lWitnesses H. E. CrrAsn, Arron M. CANNON.

Copies of this patent may be obtained for five cents each, by addressing the Commissioner of Patents, Washington, D. C. 

